Quantum double Schubert polynomials represent Schubert classes
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- by Thomas Lam and Mark Shimozono PDF
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Abstract:
The quantum double Schubert polynomials studied by Kirillov and Maeno, and by Ciocan-Fontanine and Fulton, are shown to represent Schubert classes in Kim’s presentation of the equivariant quantum cohomology of the flag variety. Parabolic analogues of quantum double Schubert polynomials are introduced and shown to represent Schubert classes in the equivariant quantum cohomology of partial flag varieties. This establishes a new method for computing equivariant Gromov-Witten invariants for partial flag varieties. For complete flags Anderson and Chen have announced a proof with different methods.References
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Additional Information
- Thomas Lam
- Affiliation: Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan 48109
- MR Author ID: 679285
- ORCID: 0000-0003-2346-7685
- Email: tfylam@umich.edu
- Mark Shimozono
- Affiliation: Department of Mathematics, MC0151, 460 McBryde Hall, Virginia Tech, 225 Stanger Street, Blacksburg, Virginia 24061
- Email: mshimo@vt.edu
- Received by editor(s): October 22, 2011
- Received by editor(s) in revised form: April 17, 2012
- Published electronically: December 11, 2013
- Additional Notes: The first author was supported by NSF grant DMS-0901111 and by a Sloan Fellowship.
The second author was supported by NSF DMS-0652641 and DMS-0652648. - Communicated by: Lev Borisov
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 835-850
- MSC (2010): Primary 14N35; Secondary 14M15
- DOI: https://doi.org/10.1090/S0002-9939-2013-11831-9
- MathSciNet review: 3148518